I think the Fractal Tardis Brain, since it would apparently be a
computational hierarchy, presents measurable science-fiction potential.
Each posthuman is a Jupiter brain, then the human civilization is a
meta-brain, our galaxy is a meta-meta brain... and obviously,
inter-galaxy communication bandwidth is pretty scarce, relative to
subjective time, even though the whole computational Universe is just an
angstrom across. So when Word Comes Down From On High for the first
time in a thousand subjective aeons, sent by the Intelligence that is
the incomprehensible sum of the Fractal Tardis Brain... then now would
be a good time to come up with a story idea.

Of course, the human meta-brain would be very new as the story opens,
perhaps only twenty subjective years old, with most of the would-be
posthumans still slowly growing into their new computational power. You
couldn't write about the ancient brains or the Fractal Tardis
Intelligence itself unless you were Greg Egan or something.